Aspecto mensurable

Eight alloys used for this investigation were melted using induction iron,

ferrosilicon, electrolytic manganese, pure aluminum, and carbon in the form of graphite. An argon cover gas was used to shield the melt and calcium wire additions were made to modify oxide inclusions and remove sulfur. Composition was both verified by optical emission spectroscopy and adjusted prior to tapping the furnace into a ladle. A modified ladle using a ceramic dam to force liquid from below the surface to form the pouring stream in a manner similar to a teapot was used for pouring the steel. All alloys were cast with 150K (150 C°) superheat into phenolic no-bake sand molds to form multiple Y- blocks each with dimensions measuring 12.6 x 6 x 1.7 cm. The upper Y-portion of the Y-block acts as a riser, but this was also attached to a Foseco KALPUR insulated riser with a diameter of 13.5 cm and height of 15.3 cm to ensure the soundness of the lower leg of the Y-block casting. The reported chemical analyses were obtained by ion coupled plasma spectrometry after sample dissolution in hydrochloric and nitric acid. Carbon and Nitrogen contents were determined using a LECO CS6000 and a LECO TC500

combustion analyzers, respectively. Alloy composition, calculated room temperature ISFE and martensite start temperatures are listed in Table I. The martensite start

temperatures were calculated according to the works of [31, 32]. For brevity alloys will be designated by the room temperature (298K, 25 °C) calculated ISFE values (bulk composition) and designated in the form # SFE. Stacking fault energies were calculated using Olson and Cohen’s equation [41] shown below as eq (2)

2 /

( / ) ( ) 2

SFE mJ m =nρ ∆Gγ ε→ + σγ ε (2)

The driving force for transformation, ΔGγ→ε_{, was obtained using an updated}

regular solution model [31], n=2, ρ calculated using alloy chemistry and Vegard’s law for the planar atomic density of the {111}γ, and σγ/ε is the interfacial energy between the γ-

austenite and ε-martensite, which was held constant at 10 mJ/m2_{. The start temperature}

for the ε-martensite was calculated by determining the temperature at which SFE = 0 mJ/m2 _{for the case where n = 4 [31]. Themartensite start temperature, , was}

calculated according to the work by Field and Van Aken [32], where the strain energy of

transformation, ( ) was balanced against the chemical driving force ( )

according to eq. (3) and eq. (4).

Chem str G Gγ α→ ∆ + ∆ = 0 (3)

( )

2

(

)

14.8 0.013 J mol Str Gγ α→ E δ T ∆ = Ω − (4)

where ∆G_Chemγ α→ is calculated according to a modified regular solution model described in Field et al. [32]. Ω is the molar volume for iron of 7.15*10-6 _(m3/mol), δ is the lattice

misfit between the γ-austenite and α-martensite with an approximate strain of 1.11*10-2

(m/m), T is the temperature in Kelvin and E is the modulus in units of Pa. The start temperature for the α-martensite was calculated by determining the temperature where eq. (2) is true.

Table I. Composition and the calculated start temperature for the ε and α martensites Alloy

Composition (wt. pct.) Calculated Parameters

Mn Si Al C N Ms ε _{in K} (°C) Msα in K (°C) 13.3 SFE 13.9 2.07 2.01 0.09 0.012 284 (11) 397 (124) 13.0 SFE 11.1 1.37 1.49 0.27 0.018 274 (1) 371 (98) 7.8 SFE 15.1 1.95 1.40 0.08 0.017 311 (38) 424 (151) 5.0 SFE 14.3 2.97 0.89 0.16 0.022 360 (87) 428 (155) -0.2 SFE 10.2 2.38 0.30 0.17 0.024 387 (114) 417 (144) -1.8 SFE 11.5 2.46 0.38 0.11 0.029 400 (127) 383 (110) -2.1 SFE 13.8 2.01 0.40 0.10 0.028 405 (132) 381 (108) -2.2 SFE 13.0 1.57 0.45 0.10 0.045 404 (131) 354 (81)

The steel castings were normalized at 1373K (1100 °C), held at temperature for 2 hours, and air cooled to 298K (25 °C). Castings were milled to an orthogonal prism of dimensions 15.5 x 125 x 50 mm3 _{and hot rolled sequentially by heating to 1223K}

(950°C), rolling, and reheating to 1223K (950 °C). This was repeated to obtain a hot band gauge of 2.5 mm. A total hot reduction of 87.2 ± 6.8 pct. was accomplished and an exit temperature of 1068 ± 15K (775 °C) was measured after the final roll pass to obtain the desired hot band thickness. Hot band tensile properties were measured to determine a target range for cold rolling. Experience processing these alloys suggested that the cold rolling reduction be limited to a range of two to three times the total elongation measured for the hot band condition. Alloys were cold rolled using a Stanat TA 315 in a 4-high roll configuration. Industrial batch annealing was mimicked by placing the cold rolled sheet into stainless steel bags and heated to 873K (600 °C) at a rate of 20K/min, allowed to equilibrate at temperature, holding for 20 hours, and air cooled to 298K (25 °C) at an average rate of 10K/min. Gray iron machining chips were added to the stainless steel bags to provide atmosphere protection.

Tensile bars were cut from both the hot band and batch annealed materials parallel to the rolling direction and the gage edge was milled to produce a standard ASTM E8 [42] tensile bar with a gage length of 50 mm and gage width of 12.5 mm. Gage width surfaces were not ground or machined. Tensile tests were conducted at room temperature and Young’s modulus was determined using a clip-on extensometer. Tests were performed in displacement control at a rate of 0.01 mm/sec using a 245 kN servo- hydraulic test frame. A non-contact laser extensometer was used to measure the total strain to failure. Non-metallic inclusions were characterized with an automated feature analysis using an ASPEX scanning electron microscope with an accelerating voltage 20.0 kV, magnification of 1000 x and the threshold size range was set to 0.3 – 40 μm to

determine the inclusion population of the developed steels.

X-ray diffraction (XRD) patterns were collected for all mechanically tested conditions to investigate the microstructural development during processing. XRD samples were mechanically polished to 0.1 μm using diamond paste in the Longitudinal- Transverse plane, (polished surface parallel to the rolling plane) and diffraction patterns were obtained with a Phillips X-pert diffractometer using Cu Kα radiation with a nickel filter and a flat graphite monochromator. Phase quantifications were calculated utilizing the Rietveld refinement described by Martin et al. [43] on an Fe-16Cr-6.8Mn-6.1Ni steel for ε-martensite analysis, and modified for the steel chemistry being investigated in this study. Work to correlate the total volume change from the various phases present and total tensile elongation was done on the alloys in both the hot band and batch annealed steels. The lattice parameter of the γ and α` crystalline phases were measured using x-ray diffraction. The ε-martensite lattice parameters were calculated assuming an ideal c/a

ratio of 1.633, which can be justified based upon iron-manganese shape memory alloys [44]. The lattice parameter for the ε-martensite was confirmed using transmission electron microscopy. A percent change in volume was calculated according to eq (5).

100% i j i j i V V V V →  −  ∆ = _{ }   (5)

Vi _{is the volume of the initial phase and V}f _{is the volume of the final phase, the total}

volume change is then calculated by eq (6).

% % %

( _vol ) ( _{vol vol} )

Total V∆ = ∆Vγ ε→ γ + ∆Vε α→ γ +ε (6)

Specimens for electron back-scattered diffraction (EBSD) were mechanically polished with a 0.02 μm colloidal silica solution using a vibratory polisher and examined in Longitudinal-Short plane (perpendicular to both the rolling plane normal and the rolling direction). Orientation image mapping via pattern analysis was performed on a Helios Nanolab 600 using a Nordlys detector and the Aztec 3.3 software package. The electron beam was operated at an accelerating voltage of 20.0 kV and an emission current 11 nA. Orientation image maps and diffraction patterns were tilt corrected for the system geometry. Degree of recrystallization was determined using the post processing software Channel 5 on multiple EBSD maps to produce a total measured area of 0.1 mm2, grains

containing internal misorientation greater than 5° where considered deformed, and grains with misorientation less than 1° were considered fully recovered. Grain size was

measured according to the ASTM E112 – 13 using the Heyn Lineal Intercept method. Transmission electron microscopy (TEM) analysis was performed using an FEI Tecnai F20 TEM. Thin foils for TEM analysis were analyzed in the Longitudinal-Transverse

plane and prepared using a solution of 6 pct. perchloric acid, 60 pct. methanol and 34 pct. butoxyethanol and a dual-Jet electropolishing system operating at 243K (-30 °C) utilizing a DC current of 10 - 12mA to keep a constant voltage of 20V. The electron beam was operated at an accelerating voltage of 200 kV.

3. RESULTS

Stress-strain plots of the hot band and annealed condition are shown in Figure 2. A summary of the tensile properties in both conditions are listed in Table II.

Microstructural characterization as performed by XRD to determine phase percentages are shown in Table III. Only alloys with positive stacking fault energies exhibit two sequential stages or rates of work hardening in the hot band materials: an initial stage with a low work hardening rate typically associated with ε-martensite formation and a subsequent rapid work hardening rate during the formation of α-martensite as shown in Figure 2(a). The observation of two different rates of work hardening is often described as an inflection in the stress strain curve, but should not be confused with a yield point elongation phenomenon. Hot band steels containing more than 30 pct. γ-austenite (and SFE > 0) produce a yield strength less than 380 MPa, a low work hardening rate (n~0.05), and elongations on the order of 3-7% prior to the onset of rapid work

hardening. After cold working and annealing alloys with a bulk ISFE less than 13 mJ/m2

exhibit an inflection in the stress versus strain plot shown in Figure 2(b). From Table III it is also noted that the alloys with a bulk ISFE ≥ 7.8 mJ/m2 do not contain any ε-

martensite in the starting microstructure. To determine if these alloys exhibited the two- stage TRIP phenomenon XRD was performed on partially strained sections of the tensile

bar and is shown in Figure 3 for the 7.8, 13.0 and 13.3SFE alloys. The 7.8SFE alloy does exhibit ε-martensite formation from strains as low as 5 pct whereas XRD patterns of the 13.0SFE and 13.3SFE alloys do not contain ε-martensite in either the partially strained or failure strain condition. From this result it can be deduced that the 13.0 and 13.3SFE alloys are not two-stage TRIP alloys.

.

Fig. 2. Stress-strain graph of the (a) hot band and (b) cold worked and annealed steels

Table II. Mechanical properties of the hot band and processed steel with grain size measured by the mean linear intercept.

Alloy

Hot Band Cold Worked and Annealed YS (MPa) UTS (MPa) ef (%) Grain Size L3 (μm) Cold Work (%) YS (MPa) UTS (MPa) ef (%) Grain Size L3 (μm) 13.3 SFE 330 1220 36.4 11.7 65.1 880 1060 42.6 0.48 13.0 SFE 450 785 19.1 12.2 55.0 1120 1330 26.5 0.68 7.8 SFE 380 1250 31.9 13.9 66.4 850 1160 41.3 0.35 5.0 SFE 205 1400 33.7 23.0 69.3 595 1370 33.7 1.56 -0.2 SFE 260 1840 12.9 16.2 35.6 840 1400 34.1 0.34 -1.8 SFE 210 1570 13.6 17.2 33.2 790 1300 27.5 0.50 -2.1 SFE 240 1300 21.0 10.7 53.6 500 1320 24.8 1.31 -2.2 SFE 255 1340 28.0 10.6 57.1 615 1450 27.7 1.23

Table III. Phase quantities of the hot band and processed steel according to x-ray diffraction.

Alloy

Hot Band Cold Worked and Annealed γ (vol%) ε (vol %) α (vol %) γ (vol%) ε (vol %) α (vol %) 13.3 SFE 95 0 5 64 0 31 13.0 SFE 94 0 6 81 0 19 7.8 SFE 79 0 21 60 0 40 5.0 SFE 93 7 0 64 30 6 -0.2 SFE 20 26 54 32 10 58 -1.8 SFE 24 24 52 34 13 53 -2.1 SFE 14 45 41 67 14 19 -2.2 SFE 36 21 43 64 33 3 Fig. 3. X-ray diffraction of the partially strained (a) 7.8 SFE, (b) 13.0 SFE and (c) 13.3

SFE alloys, with the peak positions for the γ-austenite, α-ferrite/martensite and ε- martensite labeled

The hot band 13.0SFE alloy failed before the onset of necking while the 5.0SFE, - 0.2SFE, and -2.1SFE alloys exhibit limited (< 1.5 pct.) post necking ductility. In

addition, neither the batch annealed 5.0 or -2.2 SFE alloys exhibited necking prior to failure. The density (#/mm2) and area coverage (μm2/mm2) of non-metallic inclusions are shown in Table IV. The inclusion family with the highest density for nearly all of the alloys is AlN with the exception of 5.0 SFE and -1.8 SFE steels. The 5.0 SFE alloy has a

higher density of MnS type inclusions and the -1.8SFE alloy contains a majority of its inclusions as MnO – SiO2 type inclusions. The AlN content shows a correlation to the

total N content of the steel, with an increase in N associated with an increase in AlN; this is most directly observed in the -2.2 SFE alloy having the highest nitrogen content (0.045 wt. pct.) and the highest density of aluminum nitrides.

Table IV. Inclusion density (ρ) measured as number/mm2 _{and area fraction (ppm)}

measured in μm2_/mm2 _{of non-metallic inclusions measured using the ASPEX automated}

feature analysis.

EBSD-OIM was utilized to quantitatively determine the grain size and phase constitution of the hot band and batch annealed alloys. EBSD-OIM phase maps showing grain size are shown in Figure 4(a) for the -2.2 SFE and Figure 4(b) for the 13.3 SFE steels in the hot band condition. The cold worked and annealed steels exhibit a high degree of microstructural refinement as shown in Figure 5 for the eight alloys tested. Two types of microstructures were developed after batch annealing. The 13.3, 13.0, 7.8, -0.2, and -1.8SFE alloys produced microstructures consistent with an intercritical anneal to obtain a γ + α-ferrite structure and these steels exhibit the highest degree of

microstructural refinement. The 5.0, -2.1, and -2.2SFE alloys exhibited a larger grained (>2 μm) γ-austenite with athermal ε, and α-martensite and it is understood that the

microstructure at 873K (600 °C) for these three alloys was nearly 100% γ-austenite. The average mean free path (L3) between phase boundaries measured in the batch annealed

(cold worked and annealed) steel ranged from 320 nm to 1.3 μm.

To better determine the lattice parameter of the three phases of interest γ, ε, and α transmission electron microscopy (TEM) was utilized. A TEM micrograph is shown for the -2.2SFE steel in Figure 6 with the associated diffraction patterns. TEM was utilized to confirm the ε-martensite phase and determine the lattice parameters: a = 2.62, c = 3.96 Ǻ, and c/a=1.51. A Shoji-Wasserman orientation relationship was observed between the parent γ-austenite and the ε-martensite and is in agreement with previous work on the γ, ε, and α orientation relationships observed for athermal martensites [45] and martensites formed during straining [28],

Fig. 4. EBSD-OIM of the hot band (a) -2.2 SFE (Si/Al=3.49) where prior γ-austenite grain boundaries are darkened and (b) 13.3 SFE (Si:Al=1.03) steels. γ-austenite is green

Fig. 5. EBSD-OIM map of the cold worked and annealed steel (a) 13.3 SFE, (b) 13.0 SFE, (c) 7.8 SFE, (d) 5.0 SFE, (e) -0.2 SFE, (f) -1.8 SFE, (g) -2.1 SFE, and (h) -2.2 SFE

alloys. γ-austenite is green ε-martensite is red and α-ferrite is blue.

Fig. 6. Transmission electron micrograph of the -2.2 SFE alloy showing the two-stage TRIP products of ε-martensite and α-martensite and the diffraction patterns utilized for

A Hall-Petch grain size dependence for yield strength is graphed in Figure 7 for the eight alloys tested and 43 additional alloys from literature [11, 13, 15, 40, 46-57] with grain diameters ranging from 30-0.30 μm. Data was taken from austenitic stainless steel, dual-phase α-martensite/α-ferrite, and medium-Mn steels. A linear fit is shown for the data presented in this study, but the 13.0 SFE alloy was excluded because the grain size was bimodal. Figure 7(b) compares the grain size to yield strength relationship for the alloys presented in this study and previously reported medium-Mn steels. The Hall-Petch grain size relationship shown in Figure 7 is very similar to that reported by Lee et al. [17] as shown in eq (1) with a similar grain boundary hardening term, K, (393 MPa•μm1/2 versus 332 MPa•μm1/2) and friction stress, σ0, (184 MPa versus 223 MPa) and is

discussed in greater detail below.

Fig. 7. (a) Comparison of the Hall-Petch inverse root grain size relationship of alloys produced in this study to reported austenitic stainless steels (triangles), dual-phase steels

(squares), and medium-Mn steels (circles). (b) Hall-Petch relationship for medium-Mn steels and the steels presented in this work. The line fit is restricted to measurements of

this study and is the same in both graphs. The 13.0 SFE alloy was excluded due to the highly bimodal grain size.

From the EBSD-OIM mapping the degree of recovery/recrystallization was measured for the hot band condition to understand the role of Si and Al on the tensile behavior of these steels. The degree of recovery/recrystallization was measured from multiple maps on each specimen to obtain a total map size of 0.1 ± 0.02 mm2 area. A

representative phase map and recovery/recrystallization map of the 7.8SFE steel are shown in Figure 8, and it is observed that there are twinned γ-austenite grains in the structure; however, many of the annealing twins appear bent and the grain aspect ratio shows an elongation parallel to the rolling plane. The volume pct.

recovered/recrystallized defined as less than 1° of misorientation within the grain and deformed defined as greater than 5° of misorientation within the grain relative to the Si:Al ratio is shown in Figure 9 with the uncertainty measured to a 95% confidence level. In general, a non-linear behavior is found showing that a greater resistance to

recovery/recrystallization is observed with increasing Si/Al ratio.

Fig. 8. (a) phase map of the 7.8SFE alloy in the hot band condition where green is γ- austenite and blue α-ferrite/martensite. (b) recrystallization map of the 7.8SFE alloy where blue grains are defined as recrystallized and red grains are defined as substructured

Fig. 9. The state of deformation measured according to EBSD, volume fraction of both the recrystallized and deformed grains are determined by the mean angular distribution as

a function of silicon to aluminum ratio.

A Q-R factorization to obtain a least squares fit was used to determine an empirical relationship between the chemistry and ultimate tensile strength and total elongation for the batch annealed steels exhibiting two-stage TRIP behavior, i.e. alloys with ISFE less than 10 mJ/m2_{. The derived relationships are shown in eq. (7,8) where x} i

represents weight percent alloying element “i”, it should be noted that carbon and nitrogen have large positive effect upon the ultimate strength. A comparison of the calculated and measured strength is shown in Figure 10 and a relative error of ±0.05% was determined for the tested materials.

(

) 2579*( ) 13.3*(

_{C Mn}

) 41.7 *(

_Si

) 29.4*(

_Al

) 7818*(

_N

) 747

UTS MPa

=

x

+

x

−

x

−

x

+

x

+

(7)

Partitioning of the alloying elements during the intercritical annealing at 873K (600 °C) heat treatment of the steels occurs and can be used to differentiate α-ferrite formed during the 873 K (600°C) anneal and α-martensite. Figure 11 shows the

partitioning of Al and Mn for the 13.3 SFE and 5.0 SFE alloys. Energy-dispersive x-ray spectroscopy (EDS) mapping was performed during EBSD analysis and reveals that α- ferrite grains formed during annealing are rich in aluminum and lean in Mn. Thus regions identified as α-phase that do not show alloy partitioning can be identified uniquely as α- martensite as shown in Figure 11(b) and are highlighted by arrows in the figure. There are equiaxed α grains, as well as lenticular α crystals within ε-martensite bands, and both are shown in blue. Accompanying EDS maps allow the α-ferrite grains to be

differentiated from the α-martensite: equiaxed α-ferrite grains are denuded in manganese and rich in aluminum as a result of solute partitioning during intercritical annealing. Athermal α-martensite could not be differentiated by chemistry and was typically observed within the ε-martensite bands as reported by Field and Van Aken [1] and De Cooman et al. [26]. A summary of the compositions measured from EDS analysis are shown in Table V. Equilibrium calculations performed using FactSage 7.0 with the FSstel database are also included in Table V for reference. To better replicate the composition of the α-ferrite and γ-austenite composition using the thermodynamic software a temperature was determined to reproduce the measured α-ferrite volume fraction from Table IV and adjustments were made from the EBSD analysis if only α- martensite was observed as was the case with the -2.2SFE steel. It was also assumed that the total γ-austenite at the batch annealing temperature included the athermal ε-martensite that formed upon cooling. Carbon and nitrogen reported in Table V are calculated

assuming full partitioning to the γ-austenite and the absence of AlN. The average calculated temperature that matched the measured α-ferrite was found to be 808 ± 17K (535 °C). The 65K (65 C°) difference in temperature between calculated and

experimental annealing temperature to match the α-ferrite content is likely due to (1) the alloy systems are non-dilute and (2) the kinetics for substitutional diffusion are sluggish at the intercritical annealing temperature and paraequilibrium partitioning might not have been obtained in the 20 hour treatment.

Fig. 10. Graphical comparison of the calculated properties to the measured values showing a fit of ± 0.05% with alloys exhibiting two-stage TRIP behavior, ( ISFE < 10

mJ/m2)

Fig. 11. (a) An EBSD-OIM map and the distribution of Mn and Al, in 13.3 SFE alloy and (b) EBSD-OIM map and the distribution of Mn in the 5.0 SFE alloy where α- martensite is highlighted by black arrows in the EBSD-OIM map and the α-ferrite is highlighted by white arrows in the EDS maps. α-ferrite/α-martensite (blue) grains show

increased concentration of aluminum and reduced concentration of manganese, and conversely for the γ-austenite (green).

The total elongation was correlated to the lattice parameter and the calculated volume change associated with the two martensitic reactions determined according to eq (5) and eq 6) and is shown in Figure 12. Two parallel trends are observed. The alloys

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